Pairings and twisted products (Q1582284)

The authors introduce the notion of pairing between two bialgebras over a commutative ring \(k\). Using this pairing a twisting of the multiplication of an algebra is constructed. The skew pairing studied by \textit{Y.~Doi} and \textit{M.~Takeuchi} [Commun. Algebra 22, No. 14, 5715-5732 (1994; Zbl 0821.16038)] and smash product are special cases of the theory developed here. The coalgebraic version is also considered and examples are given.